抖阴APP导航

Explore electricity, magnetism, thermodynamics, and quantum physics, providing a strong foundation in classical and modern physics. You will learn about electric and magnetic fields and forces through developing an understanding of Maxwell’s equations and their application. You will study topics in thermodynamics including heat transfer and ideal gases. You will be introduced to quantum mechanics, by examining atomic models, wave-particle duality, and the Schrödinger equation. Through problem-solving and conceptual understanding, you will develop analytical skills applicable in physics, engineering, and research. You will learn to apply mathematical models, understand physical principles, and interpret experimental results, essential for careers in scientific and technological fields.

At university, emphasis is placed on understanding general mathematical theorems. They apply in many different cases, and understanding why a result is true enables us to creatively use the underlying ideas to tackle new problems.

Study the language and structure of mathematical proofs, illustrated by results from number theory. You will see the concept of congruence of integers, which is a simplified form of arithmetic where seemingly impossible problems become solvable. In relation, you’ll encounter the abstract idea of an equivalence relation.

Sets and functions form the basic language of mathematics. You will study functions of a real variable and abstract functions between arbitrary sets, and you will explore how to count sets, both finite combinatorial arrangements and infinite sets.

You will survey the language of networks, studying relations and how to model real-world events. Throughout the module you will practise writing concise and rigorous mathematical arguments.

Interested in how mathematicians build theories from basic concepts to complex ideas, like eigenvalues and integration? Journey from polynomial operations to matrices and calculus through this module.

Starting with polynomials and mathematical induction, you will learn fundamental proof techniques. You will explore matrices, arrays of numbers encoding simultaneous linear equations, and their geometric transformations, which are essential in linear algebra. Eigenvalues and eigenvectors, which characterise these transformations, will be introduced, highlighting their role in applications including population growth and Google's page rankings.

Next, we will reintroduce you to calculus, from its invention by Newton and Leibniz, to its formalisation by Cauchy and Weierstrass. You will explore sequence convergence, techniques for evaluating limits, and key continuity tools like the intermediate value theorem. Differentiation techniques develop a geometric understanding of function graphs, leading to mastering integration methods for solving differential equations and calculating areas under curves. We conclude with a first look at vector calculus.

Modern artificial intelligence relies on multivariate calculus: every time a neural network learns, it does so by computing derivatives in high-dimensional spaces. Many real-world problems seek to understand the function of a vector, where the vector could be a position in space, a direction, or the weights of a neural network. In this module, you will explore the world of multivariate techniques and multivariate calculus, deepening your understanding of vectors, angles, curves, surfaces and volumes, multidimensional space, and alternative co-ordinate systems. You will encounter multidimensional derivatives, integrals and stationary points, and practice multidimensional analogues of techniques such as the chain rule and integration by substitution.

Throughout the module, the methods and techniques that you learn will be applied to create and solve new mathematical models for real-world problems. By the end, you will see how multivariate calculus underpins many of the techniques used in modern machine learning.

Symmetry is central to our understanding of a range of subjects, from the structure of molecules to the roots of polynomials. In this module, you will see how group theory naturally appears whenever we look at symmetry.

Using familiar examples, including symmetries of regular polygons, rotations and reflection matrices, roots of 1 in the complex plane, and permutations, you will define what makes a group and how this can provide a unifying language, highlighting connections between seemingly different subjects.

You will then transition into mathematical analysis, developing an approach to sequences, limits, and continuity that provides the foundation for calculus. Examining a range of examples, you will build your understanding of precise mathematical reasoning and gain an appreciation for the importance of proof, generalisation and abstraction.

Throughout the module, you will develop the ability to approach problems in both an analytical and creative way, preparing you for more advanced study.

We introduce you to the fundamental nature of Physics and teach you key skills in the use of experiment and uncertainty, units, and dimensional analysis. You will study topics such as Newton’s laws of motion, rotation of rigid bodies and the gravitational force. You will also be introduced to more advanced concepts such as special relativity and Lagrangian mechanics. You will apply some of these concepts to astronomical problems such as determining escape speed, and the motion of satellites and planetary orbits. You will learn about some exotic phenomena like black holes and dark matter.